Spain's smaller regional lenders, or cajas, will start a roadshow aimed at reassuring investors after the test results showed five of their peers among the seven banks that failed, and several more close to failing.
Problems among the cajas have long been flagged, however, and are being remedied.
The euro was little changed in the absence of any real shocks in the test of whether 91 banks in 20 countries could withstand another recession in the next two years.
Critics said the test was too soft – shown by the banks that failed needing just 3.5bn euros ($4.5bn).
However, “most people are going to be absolutely fine,” said Ian Henderson, who runs a global financials fund for JP Morgan. “We've already recapitalised most of the European banks anyway with huge amounts of money. Let's get on with life.”
With so few banks failing, attention was on 17 who only scraped a pass, some of whom may opt to raise cash if the test fails to reduce their funding costs or soothe worries about risks, analysts said.
“Those that are at the margin may as well raise equity to dampen down fears … The sums of money involved are really relatively small,” Henderson said.
German banks, including Deutsche Bank, were criticised for not providing as much information as rivals about their exposure to sovereign debt in the eurozone – the major worry that prompted the tests.
“You have to take these tests with a pinch of salt,” said Jonathan Cavenagh, currency strategist at Westpac, Sydney. “Sovereign debt problems remain, funding constraints for their banks are still there and these have the potential to weigh on the euro.”
Sources familiar with the discussions said Germany fought hard behind closed doors to limit the extent of disclosure.
Even so, investors now have more detail on banks' holdings of sovereign debt than they had before.
If the minimum for banks to pass the test had been set at a Tier 1 capital ratio of eight percent, rather than ix percent, an extra 27 billion euros ($35bn) of capital would have been needed, analysts at Morgan Stanley estimated.
About 40 percent of that would have been needed from German and Italian banks, it said.
Some of those banks are already making strides to raise capital, including Italy's Banca Monte dei Paschi di Siena and Banco Popolare, so they are unlikely to need more government aid. Deutsche Postbank, Germany's largest retail bank by clients, said it will continue with a plan to rebuild capital, included halting dividends.
The subdued response to the tests in Europe was a far cry from early May when global markets feared Greece's debt crisis might spread like wildfire through Europe and beyond.
Stronger-than-expected economic data suggesting the eurozone will avoid a double-dip recession, despite fiscal austerity measures, have also helped revive investor confidence in Europe.
The details from the tests should enable investors critical of the official results to run their own risk simulations to gauge a counterparty's solidity.
That should help reopen the interbank lending market, which partially froze at the height of the euro zone debt crisis and has remained tight on fears banks have been hiding exposures.
Credit markets showed a small improvement in banks' funding costs, but the real test will come when second and third tier banks try to move away from dependency on central bank funding.
Europe is aiming to repeat the boost given to US banks early last year from a health check on that sector, although the European test has been conducted much later in the cycle.
European banks have already raised about 300 billion euros since the start of the crisis – including 34 banks taking 170 billion euros from governments – whereas the US tests kick-started the fundraising.
Investors chastised EU authorities for refusing to test the impact of a debt default by Greece. But European Central Bank governing council member Christian Noyer said eurozone states “have put several hundreds of billions of euros on the table with the support of the IMF to make this hypothesis completely excluded”.